Question: Multiply the following complex numbers: $({5+4i}) \cdot ({2+i})$
Solution: Complex numbers are multiplied like any two binomials. First use the distributive property: $ ({5+4i}) \cdot ({2+i}) = $ $ ({5} \cdot {2}) + ({5} \cdot {1}i) + ({4}i \cdot {2}) + ({4}i \cdot {1}i) $ Then simplify the terms: $ (10) + (5i) + (8i) + (4 \cdot i^2) $ Imaginary unit multiples can be grouped together. $ 10 + (5 + 8)i + 4i^2 $ After we plug in $i^2 = -1$ , the result becomes $ 10 + (5 + 8)i - 4 $ The result is simplified: $ (10 - 4) + (13i) = 6+13i $